# Engineering Electromagnetics / Edition 2

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### Overview

The applications involving electromagnetism are so pervasive that it is difficult to estimate their contribution to modern life: generation and transmission of electric energy, electric motors and actuators, radio, television, magnetic information storage, and even the mundane little magnet used to hold papers to the refrigerator all use electromagnetic fields.

This text not only provides students with a good theoretical understanding of electromagnetic field equations but it also treats a large number of applications. No topic is presented unless it is directly applicable to engineering design or unless it is needed for the understanding of another topic.

Included in this new edition are:

More than 400 examples and exercises, exercising every topic in the book

600 end-of-chapter problems, many of them applications or simplified applications

A new chapter introducing numerical methods into the electromagnetic curriculum discusses the finite element, finite difference and moment methods.

The book is a comprehensive two-semester textbook. It is written in simple terms with all details of derivations included and all steps in solutions listed. It requires little beyond basic calculus and can be used for self-study. The wealth of examples and alternative explanations makes it very approachable by students.

Nathan Ida, Ph.D. is Professor of Electrical and Computer Engineering at the University of Akron. He serves on the editorial board for four international journals and is a senior member of the Institute of Electrical and Electronics Engineers, Magnetics, Microwaves, Antenna and Propagation Societies.

"...provides students with a good theoretical understanding of electromagnetic field equations, while treating a large number of applications...covers electrostatics, magnetism, electric motors & transformers, & electromagnetic waves.

### Product Details

• ISBN-13: 9780387201566
• Publisher: Springer New York
• Publication date: 5/18/2004
• Edition description: 2nd ed. 2004. Corr. 2nd printing 2007
• Edition number: 2
• Pages: 1254
• Product dimensions: 7.26 (w) x 9.46 (h) x 1.94 (d)

Preface
1 Vector Algebra
1.1 Introduction
1.2 Scalars and Vectors
1.2.1 Magnitude and Direction of Vectors: The Unit Vector and Components of a Vector
1.2.3 Vector Scaling
1.3 Products of Vectors
1.3.1 The Scalar Product
1.3.2 The Vector Product
1.3.3 Multiple Vector and Scalar Products
1.4 Definition of Fields
1.4.1 Scalar Fields
1.4.2 Vector Fields
1.5 Systems of Coordinates
1.5.1 The Cartesian Coordinate System
1.5.2 The Cylindrical Coordinate System
1.5.3 The Spherical Coordinate System
1.5.4 Transformation from Cylindrical to Spherical\penalty \@M \ Coordinates
1.6 Position Vectors
2 Vector Calculus
2.1 Introduction
2.2 Integration of Scalar and Vector\penalty \@M \ Functions
2.2.1 Line Integrals
2.2.2 Surface Integrals
2.2.3 Volume Integrals
2.3 Differentiation of Scalar and Vector\penalty \@M \ Functions
2.3.1 The Gradient of a Scalar Function
2.3.2 The Divergence of a Vector Field
2.3.2.1 Divergence in Cartesian Coordinates
2.3.2.2 Divergence in Cylindrical and Spherical Coordinates
2.3.3 The Divergence Theorem
2.3.4 Circulation of a Vector and the Curl
2.3.4.1 Circulation of a Vector Field
2.3.5 Stokes'Theorem
2.4 Conservative and Nonconservative\penalty \@M \ Fields
2.5 Null Vector Identities and Classification of Vector Fields
2.5.1 The Helmholtz Theorem
2.5.2 Second-Order Operators
2.5.3 Other Vector Identities
3 Coulomb's\penalty \@M \ Law and the Electric Field
3.1 Introduction
3.2 Charge and Charge Density
3.3 Coulomb's Law
3.4 The Electric Field Intensity
3.4.1 Electric Fields of Point Charges
3.4.1.1 Superposition of Electric Fields
3.4.1.2 Electric Field Lines
3.4.2 Electric Fields of Charge Distributions
3.4.2.1 Line Charge Distributions
3.4.2.2 Surface Charge Distributions
3.4.2.3 Volume Charge Distributions
3.5 The Electric Flux Density: An\penalty \@M \ Initial\penalty \@M \ Definition
3.6 Applications
3.7 Experiments
4 Gauss's\penalty \@M \ Law and the Electric\penalty \@M \ Potential
4.1 Introduction
4.2 The Electrostatic Field: Postulates
4.3 Gauss's Law
4.3.1 Applications of Gauss's Law
4.3.1.1 Calculation of the Electric Field Intensity
4.3.1.2 Calculation of Equivalent Charges
4.4 The Electric Potential
4.4.1 Electric Potential due to Point Charges
4.4.2 Electric Potential due to Distributed Charges
4.4.3 Calculation of Electric Field Intensity from Potential
4.5 Materials in the Electric Field
4.5.1 Conductors
4.5.1.1 Electric Field at the Surface of a Conductor
4.5.2 Dielectric Materials
4.5.3 Polarization and the Polarization Vector
4.5.4 Electric Flux Density and Permittivity
4.5.4.1 Linearity, Homogeneity, and Isotropy
4.5.5 Dielectric Strength
4.6 Interface Conditions
4.6.1 Interface Conditions Between Two Dielectrics
4.6.2 Interface Conditions Between Dielectrics and\penalty \@M \ Conductors
4.7 Capacitance
4.7.1 The Parallel Plate Capacitor
4.7.2 Capacitance of Infinite Structures
4.7.3 Connection of Capacitors
4.8 Energy in the Electrostatic Field: Point\penalty \@M \ and\penalty \@M \ Distributed Charges
4.8.1 Energy in the Electrostatic Field: Field Variables
4.8.2 Forces in the Electrostatic Field: An Energy Approach
4.9 Applications
4.1 Experiments
5 Boundary\penalty \@M \ Value Problems: Analytic Methods of Solution
5.1 Introduction
5.2 Poisson's Equation for the Electrostatic Field
5.3 Laplace's Equation for the Electrostatic Field
5.4 Solution Methods
5.4.1 Uniqueness of Solution
5.4.2 Solution by Direct Integration
5.4.3 The Method of Images
5.4.3.1 Point and Line Charges
5.4.3.2 Charged Line over a Conducting Plane
5.4.3.3 Multiple Planes and Charges
5.4.3.4 Images in Curved Geometries
5.4.4 Separation of Variables: Solution to Laplace's\penalty \@M \ Equation
5.4.4.1 Separation of Variables in Cartesian Coordinates
5.4.4.2 Separation of Variables in Cylindrical Coordinates
5.5 Experiments: The Method of Images
6 Boundary\penalty \@M \ Value Problems: Numerical (Approximate) Methods
6.1 Introduction
6.1.1 A Note on Computer Programs
6.2 The General Idea of Numerical\penalty \@M \ Solutions
6.3 The Finite Difference Method: Solution to the Laplace\hfill\ break and Poisson Equations
6.3.1 The Finite Difference Approximation: First-Order\penalty \@M \ Derivative
6.3.2 The Finite Difference Approximation: Second-Order
6.3.3 Implementation
6.3.3.1 Implicit Solution
6.3.3.2 Explicit Solution
6.3.4 Solution to Poisson's Equation
6.4 The Method of Moments: An\penalty \@M \ Intuitive\penalty \@M \ Approach
6.5 The Finite-Element Method: Introduction
6.5.1 The Finite Element
6.5.1.1 The Triangular Element
6.5.2 Implementation of the Finite Element Method
7 The\penalty \@M \ Steady Electric Current
7.1 Introduction
7.2 Conservation of Charge
7.3 Conductors, Dielectrics, and Lossy\penalty \@M \ Dielectrics
7.3.1 Moving Charges in an Electric Field
7.3.2 Convection Current and Convection Current Density
7.3.3 Conduction Current and Conduction Current Density
7.4 Ohm's Law
7.5 Power Dissipation and Joule's Law
7.6 The Continuity Equation and Kirchhoff's Current Law
7.6.1 Kirchhoff's Current Law
7.7 Current Density as a Field
7.7.2 Kirchhoff's Voltage Law
7.8 Interface Conditions for Current\penalty \@M \ Density
7.9 Applications
7.1 Experiments
8 The Static Magnetic Field
8.1 Introduction
8.2 The Magnetic Field, Magnetic Field Intensity,\hfill\ break and Magnetic Flux Density
8.3 The Biot--Savart Law
8.3.1 Applications of the Biot--Savart Law to\penalty \@M \ Distributed\penalty \@M \ Currents
8.4 Ampere's Law
8.5 Magnetic Flux Density and Magnetic\penalty \@M \ Flux
8.6 Postulates of the Static Magnetic Field
8.7 Potential Functions
8.7.1 The Magnetic Vector Potential
8.7.2 The Magnetic Scalar Potential
8.8 Applications
8.9 Experiments
9 Magnetic Materials
9.1 Introduction
9.2 Magnetic Properties of Materials
9.2.1 The Magnetic Dipole
9.2.2 Magnetization: A Model of Magnetic Properties of\penalty \@M \ Materials
9.2.3 Behavior of Magnetic Materials
9.2.3.1 Diamagnetic and Paramagnetic Materials
9.2.3.2 Ferromagnetic Materials
9.2.3.3 Other Magnetic Materials
9.3 Magnetic Interface Conditions
9.3.1 Interface Conditions for the Tangential and Normal Components of the Magnetic Field Intensity H
9.4 Inductance and Inductors
9.5 Energy Stored in the Magnetic Field
9.5.1 Magnetostatic Energy in Terms of Fields
9.6 Magnetic Circuits
9.7 Forces in the Magnetic Field
9.7.1 Principle of Virtual Work: Energy in a Gap
9.8 Torque
9.9 Applications
9.1 Experiments
10 Faraday's\penalty \@M \ Law and Induction
10.1 Introduction
10.3 Lenz's Law
10.4 Motional Electromotive Force: The\penalty \@M \ dc\penalty \@M \ Generator
10.5 Induced emf due to Transformer\penalty \@M \ Action
10.6 Combined Motional and Transformer Action Electromotive Force
10.6.1 The Alternating Current Generator
10.7 The Transformer
10.7.1 The Ideal Transformer
10.7.2 The Real Transformer: Finite Permeability
10.7.3 The Real Transformer: Finite Permeability and\penalty \@M \ Flux\penalty \@M \ Leakage
10.8 Eddy Currents
10.9 Applications
10.1 Experiments
11 Maxwell's Equations
11.1 Introduction: The\penalty \@M \ Electromagnetic\penalty \@M \ Field
11.2 Maxwell's Equations
11.2.1 Maxwell's Equations in Differential Form
11.2.2 Maxwell's Equations in Integral Form
11.3 Time-Dependent Potential Functions
11.3.1 Scalar Potentials
11.3.2 The Magnetic Vector Potential
11.3.3 Other Potential Functions
11.4 Interface Conditions for the\penalty \@M \ Electromagnetic\penalty \@M \ Field
11.4.1 Interface Conditions for the Electric Field
11.4.2 Interface Conditions for the Magnetic Field
11.5 Particular Forms of Maxwell's\penalty \@M \ Equations
11.5.1 Time-Harmonic Representation
11.5.2 Maxwell's Equations: The Time-Harmonic Form
11.5.3 Source-Free Equations
12 Electromagnetic Waves and Propagation
12.1 Introduction
12.2 The Wave
12.3 The Electromagnetic Wave Equation and Its Solution
12.3.1 The Time-Dependent Wave Equation
12.3.2 Time-Harmonic Wave Equations
12.3.3 Solution of the Wave Equation
12.3.4 Solution for Uniform Plane Waves
12.3.5 The One-Dimensional Wave Equation in Free Space and Perfect Dielectrics
12.4 The Electromagnetic Spectrum
12.5 The Poynting Theorem and Electromagnetic Power Density
12.6 The Complex Poynting Vector
12.7 Propagation of Waves in Materials
12.7.1 Propagation of Waves in Lossy Dielectrics
12.7.2 Plane Waves in Low Loss Dielectrics
12.7.3 Propagation of Plane Waves in Conductors
12.7.4 The Speed of Propagation of Waves and Dispersion
12.7.4.1 Group velocity
12.7.4.2 Velocity of Energy Transport
12.7.4.3 Dispersion
12.8 Polarization of Plane Waves
12.8.1 Linear Polarization
12.8.2 Elliptical and Circular Polarization
12.9 Applications
12.1 Experiments
13 Reflection and Transmission of Plane Waves
13.1 Introduction
13.2 Reflection and Transmission at a General Dielectric Interface: Normal\penalty \@M \ Incidence
13.2.1 Reflection and Transmission at an Air-Lossy Dielectric Interface: Normal Incidence
13.2.2 Reflection and Transmission at an Air-Lossless Dielectric Interface: Normal Incidence
13.2.3 Reflection and Transmission at an Air-Conductor Interface: Normal Incidence
13.3 Reflection and Transmission at an\penalty \@M \ Interface: Oblique Incidence on a\penalty \@M \ Conductor
13.3.1 Oblique Incidence on a Conducting Interface: Perpendicular Polarization
13.3.2 Oblique Incidence on a Conducting Interface: Parallel Polarization
13.4 Oblique Incidence on Dielectric\penalty \@M \ Interfaces
13.4.1 Oblique Incidence on a Dielectric Interface: Perpendicular Polarization
13.4.2 Oblique Incidence on a Dielectric Interface: Parallel\penalty \@M \ Polarization
13.4.3 Brewster's Angle
13.4.3.1 Brewster's Angle for Parallel Polarization
13.4.3.2 Brewster's Angle for Perpendicular Polarization
13.4.4 Total Reflection
13.5 Reflection and Transmission for Layered Materials at Normal Incidence
13.5.1 Reflection and Transmission for a Lossy Dielectric Slab at Normal Incidence
13.5.2 Reflection and Transmission for a Lossless Dielectric Slab at Normal Incidence
13.5.3 Reflection and Transmission for a Conducting Slab at Normal Incidence
13.5.4 Reflection and Transmission for a Lossless Dielectric\penalty \@M \ Slab Backed by a Perfect Conductor: Normal\penalty \@M \ Incidence
13.6 Applications
13.7 Experiments
14 Theory of Transmission Lines
14.1 Introduction
14.2 The Transmission Line
14.3 Transmission Line Parameters
14.3.1 Calculation of Line Parameters
14.3.1.1 Resistance per Unit Length
14.3.1.2 Inductance per Unit Length
14.3.1.3 Capacitance per Unit Length
14.3.1.4 Conductance per Unit Length
14.4 The Transmission Line Equations
14.5 Types of Transmission lines
14.5.1 The Lossless Transmission Line
14.5.2 The Long Transmission Line
14.5.3 The Distortionless Transmission Line
14.5.4 The Low-Resistance Transmission Line
14.6 The Field Approach to Transmission\penalty \@M \ Lines
14.7 Finite Transmission Lines
14.7.2 Line Impedance and the Generalized Reflection Coefficient
14.7.3 The Lossless, Terminated Transmission Line
14.7.4 The Lossless, Matched Transmission Line
14.7.5 The Lossless, Shorted Transmission Line
14.7.6 The Lossless, Open Transmission Line
14.7.7 The Lossless, Resistively Loaded Transmission Line
14.8 Power Relations on a General Transmission Line
14.9 Resonant Transmission Line Circuits
14.1 Applications
14.11 Experiment
15 The\penalty \@M \ Smith\penalty \@M \ Chart, \hbox Impedance Matching, and
15.1 Introduction
15.2 The Smith Chart
15.3 The Smith Chart as an Admittance Chart
15.4 Impedance Matching and the Smith Chart
15.4.1 Impedance Matching
15.4.2 Stub Matching
15.4.2.1 Single Stub Matching
15.4.2.2 Double Stub Matching
15.5 Quarter-Wavelength Transformer Matching
15.6 Experiments
16 Transients on Transmission Lines
16.1 Introduction
16.2 Propagation of Narrow Pulses on Finite, Lossless Transmission Lines
16.3 Propagation of Narrow Pulses on Finite, Distortionless\hfill\ break Transmission Lines
16.4 Transients on Transmission Lines: Long Pulses
16.5 Transients on Transmission Lines: Finite-Length Pulses
16.6 Reflections from Discontinuities
16.8 Initial Condition on Line
16.9 Experiments
17 Waveguides
17.1 Introduction
17.2 The Concept of a Waveguide
17.3 Transverse Electromagnetic, Transverse Electric,\hfill\ break and Transverse Magnetic Waves
17.3.1 Transverse Electromagnetic Waves
17.3.2 Transverse Electric (TE) Waves
17.3.3 Transverse Magnetic Waves
17.4 TE Propagation in Parallel Plate Waveguides
17.5 TM Propagation in Parallel Plate Waveguides
17.6 TEM Waves in Parallel Plate Waveguides
17.7 Rectangular Waveguides
17.7.1 TM Modes in Rectangular Waveguides
17.7.2 TE Modes in Rectangular Waveguides
17.7.3 Attenuation and Losses in Rectangular Waveguides
17.8 Other Waveguides
17.9 Cavity Resonators
17.9.1 TM Modes in Cavity Resonators
17.9.2 TE Modes in Cavity Resonators
17.1 Energy Relations in a Cavity Resonator
17.11 Quality Factor of a Cavity Resonator
17.12 Applications
18.1 Introduction
18.3 Antennas
18.4 The Electric Dipole
18.4.1 The Near Field
18.4.2 The Far Field
18.5 Properties of Antennas
18.5.3.1 Planar Antenna Radiation Pattern Plots
18.5.3.2 Rectangular Power Pattern Plots
18.5.3.3 Beamwidth
18.5.5 Antenna Directivity
18.5.6 Antenna Gain and Radiation Efficiency
18.6 The Magnetic Dipole
18.6.1 Near fields for the magnetic dipole
18.6.2 Far Fields for the Magnetic Dipole
18.6.3 Properties of the Magnetic Dipole
18.7 Practical Antennas
18.7.1 Linear Antennas of Arbitrary Length
18.7.1.1 The Half-Wavelength Dipole Antenna
18.7.1.2 Full- and Three-Halves-Wavelength Antennas
18.7.2 The Monopole Antenna
18.8 Antenna Arrays
18.8.1 The Two-Element Array
18.8.2 The $n$-Element Linear Array
18.9 Reciprocity and Receiving Antennas
18.1 Effective Aperture
18.12 Other Antennas
18.13 Applications
Index

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